The purpose of a navigation system is to provide the user with an estimate of their time, position, velocity, and orientation. Global Navigation Satellite Systems (GNSS), like Global Positioning Systems (GPS), are designed to assist the user in estimating those quantities. However, GNSS require line of sight from the satellite to the user to provide reliable estimates. Therefore, in order to increase the robustness of the navigation system, GNSS receivers are integrated with other navigation sensors.
The conventional method is to integrate inertial navigation systems (INS) with GNSS receivers. The inertial navigation system provides the user with specific force measurements (used to estimate acceleration) and rotation rates (used to estimate position, velocity, and orientation) at a higher data rate than GNSS. However, INS suffer from errors that grow with time and require regular updates from GNSS to prevent the error growth. In a loose configuration, the INS and GNSS receiver act as independent navigation systems. Each systems' position, velocity, and orientation are filtered together to provide the user with time, position, velocity, and orientation. In a tight configuration, the INS and GNSS receiver are no longer independent. The INS provides specific force and rotation rate measurements and the GNSS provides pseudorange and pseudorange rates. These measurements are filtered together to provide the user with time, position, velocity, and orientation.
Tightly integrated GPS/INS systems typically model the errors in the pseudorange measurements as white noise or first order Gauss-Markov processes. Some approaches model the pseudorange errors as autoregressive processes. The disadvantage in these approaches is that the pseudorange errors are assumed to be uncorrelated with each other. However, since the GNSS signals travel from space to the user, environmental and/or geometrical factors can lead to time correlation between different pseudorange errors, which these conventional approaches do not account for. A need exists for a method to exploit the time correlation between different pseudorange errors, thus producing a better position estimate than the conventional methods.